A coupling scheme was developed to couple the CFD software STAR-CCM+ v10.04 and the system code RELAP5-3D v4.2.1. In this paper the structure of the scheme is presented, together with validations for single phase flow in smooth pipes in both transient and steady state cases. Attention was also given to the problem of reconstructing the profile at the inlet of the CFD model under the hypothesis of fully developed flow. This problem arises when flow data has to be passed from the one-dimensional system code to the three-dimensional CFD software.

The flow of an electrically conducting fluid in an array of square ducts, separated by arbitrary thickness conducting walls, subject to an applied magnetic field is studied. The analytical solution presented here is valid for thick walls and is based on the homogeneous solution obtained by Shercliff (Math. Proc. Camb. Phil. Soc., vol. 49 (01), 1953, pp. 136-144). Arrangements of ducts arise in a number of applications, most notably in fusion blankets, where liquid metal is used both as coolant and for tritium generation purposes. Analytical solutions, such as those presented here, provide insight into the physics and important benchmarking and validation data for computational magnetohydrodynamics (MHD), as well as providing approximate flow parameters for 1D systems codes. It is well known that arrays of such ducts with conducting walls exhibit varying degrees of coupling, significantly affecting the flow. An important practical example is the so-called Madarame problem (Madarame et al., Fusion Technol., vol. 8, 1985, pp. 264-269). In this work analytical results are derived for the relevant hydrodynamic and magnetic parameters for a single duct with thick walls analogous to the Hunt II case. These results are then extended to an array of such ducts stacked in the direction of the applied magnetic field. It is seen that there is a significant coupling affect, resulting in modifications to pressure drop and velocity profile. In certain circumstances, counter-current flow can occur as a result of the MHD effects, even to the point where the mean flow is reversed. Such phenomena are likely to have significant detrimental effects on both heat and mass transfer in fusion applications. The dependence of this coupling on parameters such as conductivities, wall thickness and Hartmann number is studied.

This paper considers the solution of the electric field integral equation (EFIE). Hierarchical conforming bases are developed which are subsequently used in the construction of a multilevel Schwarz type preconditioner. The effectiveness of this approach is demonstrated by the computation of scattering from sub-wavelength scattering bodies. The resulting schemes are shown to be faster than conventional schemes up to an order of magnitude.

The thermal hydraulic analysis of nuclear reactors is largely performed by what are known as "System Codes". These codes predict the flows in the complex network of pipes, pumps, vessels and heat exchangers that together form the thermal hydraulic systems of a nuclear reactor. These codes have been used for many decades, and are now very well established, and given this long process of refinement, they are able to produce remarkably accurate predictions of plant behaviour under both steady and transient conditions. Modern CFD is able to produce high-quality predictions of flows in complex geometries, but only with the use of large computing resources. It would be impractical to build a CFD model of, for example, the entire primary circuit of a PWR. However, much of the primary circuit may well be able to be modelled with adequate fidelity using a cheaper one-dimensional system code, and it may only be in a limited part of the circuit that full three-dimensional effects are important. In this paper, the coupling tool present in the STAR-CCM+ v8.02 software was used, together with RELAP5-3D v4.0.3, to perform a coupled analysis of single phase flow in a circular pipe in order to evaluate Moody's friction factor. Three different cases were studied, following two different models. The first case consisted in using smooth walls for the pipe, whereas, in the second and the third ones, the roughness of the wall was set to 20 μm and 50 μm respectively. The first model consisted in using RELAP5-3D for the upstream part of the pipe and STAR-CCM+ for the downstream part. In the second model, instead, STAR-CCM+ was used for the upstream part of the pipe and RELAP5-3D for the downstream part. The results obtained with these two models have been compared with each other to check for possible incongruences. Furthermore, all the results have been compared with standalone simulations performed with RELAP5-3D and STAR-CCM+ and with experimental data (Moody's diagram).

Integral equation schemes, both EFIE and MFIE, have become a powerful tool, particularly with the development of accelerated schemes such as the fast multipole method (FMM). Key to most such treatments is the requirement to solve matrix equations iteratively, which at their core involve matrixvector multiplications. Much of the cost of such solutions then depends on the number of iterations and the cost per iteration. The vast majority of integral equations implementations employ the simplest Rao-WiltonGlisson (RWG) basis functions on triangles. High order interpolatory bases have been developed which (in principle) offer improved accuracy for a given cost. Within the current developments, the next natural step beyond high order interpolatory methods is to arrange these bases hierarchically, as already experienced within the finite element community. Of themselves hierarchical bases offer little more than their high order interpolatory counterparts. However, as has been demonstrated in finite elements it is possible to employ this hierarchical structure to great effect in the reduction of the computational cost of the underlying iterative scheme via a multilevel Schwarz type preconditioner. In this paper we attempt to apply such hierarchical bases and their associated acceleration schemes to integral equations. The results suggest that their efficacy depend strongly on the scattering regime. In particular, high frequency problems (those where the wavelength is the principal determinant of mesh size) are shown to benefit little from hierarchical functions. Unlike their finite element counterparts, equivalent p-MUS integral equation schemes appear to offer little gain, if any, over nonhierarchical schemes. On the other hand, for ̀low frequency' problems, such as scattering of objects with sub-wavelength features (where geometry is the main determinant of mesh size), there are significant improvements in performance over corresponding interpolatory schemes. Copyright &

In this paper we discuss the application of algebraic topology to computational electromagnetics. Basic homology and cohomology theory is explained in the context of numerical schemes. We will show how these concepts influence the choice of discrete spaces for both finite and boundary element methods. Spaces on simplicial manifolds (triangles, tetrahedra), cartesian product manifolds (quadrilaterals, hexahedra) and prismatic manifolds are easily constructed in the light of these topological considerations. In particular, Nedelec, Raviart-Thomas, Whitney and Rao-Wilton-Glisson type function spaces are easily obtained as special cases. This approach is not restricted to affine manifolds with results being equally valid for the general curvilinear case. In general an adjoint form of the commuting de Rham diagram is shown to hold and how this property affect convergence is discussed.

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